机器学习14—SVD学习笔记

test14.py

#-*- coding：utf-8
import sys
sys.path.append("svdRec.py")
 
import svdRec
from numpy import *
from numpy import linalg as la
 
# U, Sigma, VT = linalg.svd([[1, 1], [7, 7]])
# print(U)
# print(Sigma)
# print(VT)
 
# Data = svdRec.loadExData()
# U, Sigma, VT = linalg.svd(Data)
# print(Sigma)
#
# Sig3 = mat([[Sigma[0], 0, 0], [0, Sigma[1], 0], [0, 0, Sigma[2]]])
# res = U[:, :3]*Sig3*VT[:3, :]
# print("res:")
# print(res)
#
# myMat = mat(svdRec.loadExData())
# ecl = svdRec.ecludSim(myMat[:, 0], myMat[:, 4])
# print("ecl:")
# print(ecl)
# cos = svdRec.cosSim(myMat[:, 0], myMat[:, 4])
# print("cos:")
# print(cos)
# pears = svdRec.pearsSim(myMat[:, 0], myMat[:, 4])
# print("pears:")
# print(pears)
# myMat = mat(svdRec.loadExData())
# myMat[0, 1] = myMat[0, 0] = myMat[1, 0] = myMat[2, 0] = 4
# myMat[3, 3] = 2
# print("myMat:")
# print(myMat)
#
# tuiJian = svdRec.recommend(myMat, 2)
# print("tuiJian:")
# print(tuiJian)
#
# tuiJian1 = svdRec.recommend(myMat, 2, simMeas = svdRec.ecludSim)
# print("tuiJian1:")
# print(tuiJian1)
#
# tuiJian2 = svdRec.recommend(myMat, 2, simMeas = svdRec.pearsSim)
# print("tuiJian2:")
# print(tuiJian2)
 
# myMat = mat(svdRec.loadExData2())
# U, Sigma, VT = la.svd(mat(svdRec.loadExData2()))
# print(Sigma)
#
# Sig2 = Sigma**2
# total = sum(Sig2)
# total9 = total*0.9
# print("total9:")
# print(total9)
#
# total3 = sum(Sig2[:3])
# print("total3:")
# print(total3)
 
# svdRes = svdRec.recommend(myMat, 1, estMethod = svdRec.svdEst)
# print("svdRes:")
# print(svdRes)
 
originalMat = svdRec.imgCompress(2)
print(originalMat)
 
print("over!!!")

svdRec.py

'''
Created on Mar 8, 2011
 
@author: Peter
'''
from numpy import *
from numpy import linalg as la
 
def loadExData():
    return[[0, 0, 0, 2, 2],
           [0, 0, 0, 3, 3],
           [0, 0, 0, 1, 1],
           [1, 1, 1, 0, 0],
           [2, 2, 2, 0, 0],
           [5, 5, 5, 0, 0],
           [1, 1, 1, 0, 0]]
 
def loadExData2():
    return[[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 5],
           [0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 3],
           [0, 0, 0, 0, 4, 0, 0, 1, 0, 4, 0],
           [3, 3, 4, 0, 0, 0, 0, 2, 2, 0, 0],
           [5, 4, 5, 0, 0, 0, 0, 5, 5, 0, 0],
           [0, 0, 0, 0, 5, 0, 1, 0, 0, 5, 0],
           [4, 3, 4, 0, 0, 0, 0, 5, 5, 0, 1],
           [0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4],
           [0, 0, 0, 2, 0, 2, 5, 0, 0, 1, 2],
           [0, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0],
           [1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0]]
 
def ecludSim(inA,inB):
    return 1.0/(1.0 + la.norm(inA - inB))
 
def pearsSim(inA,inB):
    if len(inA) < 3 : return 1.0
    return 0.5+0.5*corrcoef(inA, inB, rowvar = 0)[0][1]
 
def cosSim(inA,inB):
    num = float(inA.T*inB)
    denom = la.norm(inA)*la.norm(inB)
    return 0.5+0.5*(num/denom)
 
def standEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    for j in range(n):
        userRating = dataMat[user,j]
        if userRating == 0: continue
        # test0 = dataMat[:,item].A>0
        # test1 = dataMat[:,j].A>0
        # test2 = logical_and(dataMat[:,item].A>0, dataMat[:,j].A>0)
        overLap = nonzero(logical_and(dataMat[:,item].A>0, dataMat[:,j].A>0))[0]
        if len(overLap) == 0: similarity = 0
        else: similarity = simMeas(dataMat[overLap,item], dataMat[overLap,j])
        print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal
 
def svdEst(dataMat, user, simMeas, item):
    n = shape(dataMat)[1]
    simTotal = 0.0; ratSimTotal = 0.0
    U,Sigma,VT = la.svd(dataMat)
    Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
    xformedItems = dataMat.T * U[:,:4] * Sig4.I  #create transformed items
    for j in range(n):
        userRating = dataMat[user,j]
        if userRating == 0 or j==item: continue
        similarity = simMeas(xformedItems[item,:].T, xformedItems[j,:].T)
        print('the %d and %d similarity is: %f' % (item, j, similarity))
        simTotal += similarity
        ratSimTotal += similarity * userRating
    if simTotal == 0: return 0
    else: return ratSimTotal/simTotal
 
def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
    unratedTest = nonzero(dataMat[user,:].A==0)
    unratedItems = nonzero(dataMat[user,:].A==0)[1]#find unrated items
    if len(unratedItems) == 0: return 'you rated everything'
    itemScores = []
    for item in unratedItems:
        estimatedScore = estMethod(dataMat, user, simMeas, item)
        itemScores.append((item, estimatedScore))
        # testSort = sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]
    return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]
 
def printMat(inMat, thresh=0.8):
    for i in range(32):
        for k in range(32):
            if float(inMat[i,k]) > thresh:
                print(1),
            else: print(0),
        print('')
 
def imgCompress(numSV=3, thresh=0.8):
    myl = []
    for line in open('0_5.txt').readlines():
        newRow = []
        for i in range(32):
            newRow.append(int(line[i]))
        myl.append(newRow)
    myMat = mat(myl)
    print("****original matrix******")
    printMat(myMat, thresh)
    U,Sigma,VT = la.svd(myMat)
    SigRecon = mat(zeros((numSV, numSV)))
    for k in range(numSV):#construct diagonal matrix from vector
        SigRecon[k,k] = Sigma[k]
    reconMat = U[:,:numSV]*SigRecon*VT[:numSV,:]
    print("****reconstructed matrix using %d singular values******" % numSV)
    printMat(reconMat, thresh)